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The term “dynamic” here means the dependence of the dependent variable on its past history; this is usually used to model the “state dependence” in economics. For instance, for a person who cannot find a job this year, it will be harder to find a job next year because her present lack of a job will be a negative signal for the potential employers. “Unobserved effects” means that one or some of the explanatory variables are unobservable: for example, consumption choice of one flavor of ice cream over another is a function of personal preference, but preference is unobservable.
==Continuous dependent variable==
==Formulation==▼
{{further|Panel analysis#Dynamic panel models|Arellano–Bond estimator}}
==Censored dependent variable==
==Binary dependent variable==
▲===Formulation===
A typical dynamic unobserved effects model with a [[binary data|binary]] dependent variable is represented<ref>Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 300.</ref> as:
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where c<sub>i</sub> is an unobservable explanatory variable, z<sub>it</sub> are explanatory variables which are exogenous conditional on the c<sub>i</sub>, and G(∙) is a [[cumulative distribution function]].
===Estimates of parameters===
In this type of model, economists have a special interest in ρ, which is used to characterize the state dependence. For example, ''y<sub>i,t</sub>'' can be a woman's choice whether to work or not, ''z<sub>it</sub>'' includes the ''i''-th individual's age, education level, number of children, and other factors. ''c<sub>i</sub>'' can be some individual specific characteristic which cannot be observed by economists.<ref>James J. Heckman (1981): Studies in Labor Markets, University of Chicago Press, Chapter Heterogeneity and State Dependence</ref> It is a reasonable conjecture that one's labor choice in period ''t'' should depend on his or her choice in period ''t'' − 1 due to habit formation or other reasons. This dependence is characterized by parameter ''ρ''.
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Based on the estimates for (''δ, ρ'') and the corresponding variance, values of the coefficients can be tested<ref>Whitney K. Newey, Daniel McFadden, Chapter 36 Large sample estimation and hypothesis testing, In: Robert F. Engle and Daniel L. McFadden, Editor(s), Handbook of Econometrics, Elsevier, 1994, Volume 4, Pages 2111–2245, {{ISSN|1573-4412}}, {{ISBN|9780444887665}},</ref> and the average partial effect can be calculated.<ref>Chamberlain, G. (1980), “Analysis of Covariance with Qualitative Data,” Journal of Econometrics 18, 5–46</ref>
▲* {{section link|Tobit model#Dynamic unobserved effects tobit model}}
==References==
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